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Cite this: Phys. Chem. Chem. Phys.,
2016, 18, 4112
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Adsorption and separation of binary and ternary
mixtures of SO2, CO2 and N2 by ordered carbon
nanotube arrays: grand-canonical Monte
Carlo simulations
Mahshid Rahimi,*a Jayant K. Singhab and Florian Müller-Plathea
The adsorption and separation behavior of SO2–CO2, SO2–N2 and CO2–N2 binary mixtures in bundles
of aligned double-walled carbon nanotubes is investigated using the grand-canonical Monte Carlo
(GCMC) method and ideal adsorbed solution theory. Simulations were performed at 303 K with nanotubes of 3 nm inner diameter and various intertube distances. The results showed that the packing with
an intertube distance d = 0 has the highest selectivity for SO2–N2 and CO2–N2 binary mixtures. For the
SO2–CO2 case, the optimum intertube distance for having the maximum selectivity depends on the
applied pressure, so that at p o 0.8 bar d = 0 shows the highest selectivity and at 0.8 bar o p o 2.5 bar,
the highest selectivity belongs to d = 0.5 nm. Ideal adsorbed solution theory cannot predict the adsorption of
the binary systems containing SO2, especially when d = 0. As the intertube distance is increased, the ideal
Received 20th October 2015,
Accepted 11th January 2016
adsorbed solution theory based predictions become closer to those of GCMC simulations. Only in the case
DOI: 10.1039/c5cp06377a
of CO2–N2, ideal adsorbed solution theory is everywhere in good agreement with simulations. In a ternary
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because of the weak interaction between N2 molecules and CNTs.
mixture of all three gases, the behavior of SO2 and CO2 remains similar to that in a SO2–CO2 binary mixture
1. Introduction
In the last decade carbon nanotubes (CNTs) have been widely
studied as adsorbents of different gases such as H2, N2, CO2,
SO2, alkanes and noble gases.1,2 This great interest in using
CNTs for gas adsorption and separation is mainly due to their
hollow cylindrical geometry, low mass density and large specific
area.3,4 In many studies, CNTs were compared with other gas
sorbents and found to have higher gas adsorption and separation. Lu et al. studied CO2 capture experimentally and showed
that CNTs are better adsorbents in terms of capacity per mass,
compared with other sorbents such as zeolites and activated
carbon.5 Diffusivities of light gases (H2 and CH4) in carbon
nanotubes and zeolites with comparable pore sizes were studied
by molecular dynamics simulations. It was found that the
diffusivity of H2 and CH4 in carbon nanotubes is orders of
magnitude faster than in zeolites.6 Using grand canonical Monte
Carlo (GCMC) simulations for CO2 and CH4 adsorption, Huang
et al. showed that CNTs have a higher selectivity for CO2/CH4
a
Technische Universität Darmstadt, Eduard-Zintl-Institut für Anorganische und
Physikalische Chemie, Alarich-Weiss-Str. 4, D-64287 Darmstadt, Germany.
E-mail: [email protected]
b
Department of Chemical Engineering, Indian Institute of Technology Kanpur,
Kanpur-208016, India
4112 | Phys. Chem. Chem. Phys., 2016, 18, 4112--4120
separation than that reported for activated carbons, zeolite 13X
and metal organic frameworks (MOFs).7
The important role of carbon porosity was revealed by
simulated SO2 adsorption isotherms on activated carbon.8 This
role is even more important in the case of CNTs because of
their well-defined structure and arrangement. Accordingly, the
optimization of the geometrical properties like the tube diameter and the intertube distance has always been a question.
Jakobtorweihen et al.9 employed GCMC simulations to investigate the adsorption of linear alkanes and alkenes on CNTs with
different tube diameters. Narrower pores were found to have
higher adsorption at low pressure ( p o 2 bar) and lower adsorption at high pressure (2 bar o p o 1000 bar). Kowalczyk and
coworkers10 used GCMC to measure the amount of CO2 adsorbed
onto CNTs and showed that the optimum diameter for having the
highest adsorption depends on the applied pressure. This result
was confirmed by our recent study of SO2 adsorption on CNTs.11
The same method has been used to measure the adsorption of
CO2 and SO2 molecules on single-walled CNTs (SWCNTs).12 The
contributions of the inner and outer adsorption were studied and
it was found out that for both molecules, the inside adsorption is
higher at low pressures. The outside adsorption becomes larger
above 10 and 2 bar for CO2 and SO2, respectively.
In CNT bundles, the intertube distance is a second geometrical parameter that can be tuned13 and it is also claimed to
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have an important effect on adsorption.14,15 Agnihotri et al.16
combined the experiment and simulations to analyze the
adsorption sites in CNT bundles. They showed that grooves
are the most favorable sites. They are completely filled already
at very low pressure. In order to measure the adsorption locally,
Bienfait and coworkers17 used neutron diffraction measurements
of different gases on CNTs. They also found grooves as the best
adsorption sites.
The ideal adsorbed solution theory (IAST) developed by Myers
and Prausnitz18 is a technique used to calculate multi-component
adsorption equilibria based on single-component adsorption
isotherms. The agreement of IAST and GCMC simulations for
the adsorption of binary mixtures of CO2/CH4/H2/N2 on various
materials, like MOFs and CNTs, was confirmed by various
groups.19–21 Cannon and coworkers22 used GCMC to study the
adsorption and selectivity of linear alkanes on closed nanotube
bundles. They found that the adsorption of the alkane mixture
agrees between IAST and simulations. Peng et al.23 showed that
the IAST prediction of CO2 and CH4 adsorption in ordered carbon
nanopipes is in good agreement with experiment. Using molecular
simulations and IAST, the selectivity of nanoporous carbon materials
for the mixture of CO2 and H2 was studied by Kumar and Rodrı́guezReinoso.24 To investigate the effects of nanopore structure, carbon
nanotubes, slit-shaped porous carbon form and a carbon model
with a disordered pore structure, were considered. The results
showed that CNTs have the highest selectivity towards CO2.
Among all the adsorption and separation studies, there are
few investigations of SO2 and its mixture with CO2. Wang and
coworkers25 used GCMC to calculate SO2–CO2 and SO2–N2
mixtures in CNT bundles with different tube diameters. They
found that among the studied diameters, 1.09 nm and 0.81 nm
show the highest selectivity for SO2–CO2 and SO2–N2 respectively.
Furthermore, they showed a decrease of selectivity with increasing
temperature. The observations of these authors were still based
on bundles of single-walled CNTs (SWCNTs) with a fixed intertube
distance. However, it is not known if such behavior also occurs
for double- or multi-walled CNT bundles. Moreover, the effect of
the intertube distance was not investigated. Finally, it would be
helpful for experimental studies to know if IAST can be used for
the adsorption of the SO2–CO2 mixture in bundles of CNTs.
In this study, we investigate the adsorption and selectivity of
binary (SO2–CO2, CO2–N2 and SO2–N2) and ternary mixtures (SO2–
CO2–N2) in bundles of double-walled carbon nanotubes (DWCNTs)
using the GCMC method. Since the influence of the tube diameter
has been exhaustively studied,11,26 the intertube distances of
DWCNT arrays are varied in order to find the optimum geometry
for each adsorption/separation situation. Predictions of the IAST
approximation are compared with the results of the simulations.
2. Model and method
Following our previous studies,14,15,26 the DWCNTs in the
simulation box are arranged on a hexagonal lattice, and periodic
boundary conditions are used in all three directions (cf. Fig. 1
of ref. 14). In the present study, DWCNTs with an inner tube
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diameter of 2R = 2.98 nm, which was found to be optimum for
single gas adsorption, are used.26 Since the adsorption isotherm
was found to be insensitive to the CNT length,11 the DWCNT
length is fixed to be 7.38 nm. The intertube distance (the surface
to surface distance between the outer layers of adjacent tubes,
i.e. d = 0 represents the case of touching DWCNTs, the distance
between the positions of their surface carbons being 0.34 nm) is
varied (d = 0 to 2 nm), since it has a stronger effect compared to
the tube diameter, and since its optimum value depends on the
applied pressure.11 The simulation box length in the direction of
the CNT axes is equal to the CNT length; the simulation box lengths
in the other two directions are adjusted to the intertube distance. In
total, there are 11 760 carbon atoms in the simulation box.
The DWCNTs are considered as rigid structures with a C–C
bond length of 0.142 nm. The Lennard-Jones potential of the
AMBER96 force field27 is used to describe DWCNTs. It has been
used in similar work.11,28 The EPM2 model of Harris and
Yung29 is used to describe CO2. In this model, CO2 is considered
as a 3-site rigid molecule with Lennard-Jones potential (sC–C =
0.2757 nm, eC–C = 0.23388 kJ mol1, sO–O = 0.3033 nm,
eO–O = 0.66837 kJ mol1) plus a set of partial point charges
(qC = 0.6512e), a fixed bond length (lC–O = 0.1149 nm) and a fixed
angle (yO–C–O = 1801). Ketko et al.30 developed an optimized
intermolecular potential for SO2 to accurately calculate the
vapor–liquid equilibria, critical properties, vapor pressure, and
heats of vaporization. This rigid model, which is used in the
present study, describes SO2 using Lennard-Jones interactions
and partial charges (sS–S = 0.339 nm, eC–C = 0.61361 kJ mol1,
sO–O = 0.305 nm, eO–O = 0.65684 kJ mol1, lS–O = 0.1432 nm,
and yO–S–O = 119.31). The N2 molecules are also modeled as
a 3-site molecule with Lennard-Jones potential plus a set of
partial point charges, a fixed bond length and a fixed angle.31
Dissimilar non-bonded interactions are calculated using the
Lorentz–Berthelot combining rules. The electrostatic interactions are calculated using the smooth-particle-mesh Ewald
(SPME) method.32
The grand canonical Monte Carlo method at constant
chemical potential m, volume V and temperature T is used to
calculate the adsorption and separation coefficients of gases.
Three Monte Carlo moves, displace, rotate, and insert/delete,
with the probability of 0.2, 0.1 and 0.7, respectively, are
implemented. The temperature is fixed at 303 K and the atomic
cutoff is 1 nm. In order to account for the non-ideality of gases,
the fugacities of the components in the bulk phases were
calculated using the Peng–Robinson equation of state (PR
EOS) for mixtures.33 For all simulation runs, 1 107 Monte
Carlo steps are used for equilibration and another 1 107
Monte Carlo steps for data collection. The output of the
simulation is the total number of gas molecules of each
component, which is converted to a common unit for adsorption, mmol of gas per gram of adsorbent and is denoted ni for
the component i. Adsorption selectivity of component i relative
to component j in a binary system is calculated using
Si =j ¼
xi
xj
yi
yj
(1)
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where xi and yi are the molar fractions of component i in the
adsorbed and bulk gas phases, respectively.
The composition of flue gas strongly depends on the type of
fuel and the combustion conditions. For instance, the flue gas
from coal-fire consists of 7 to 15% moles of CO2.34,35 In this
work, we use the molar ratio of 5 : 95, 1 : 99 and 15 : 85 in the
bulk phase for the binary mixtures of SO2–CO2, SO2–N2, and
CO2–N2, respectively.25,36–38
The ideal adsorbed solution theory (IAST) predicts multicomponent sorption equilibria from single-component isotherms.18
According to IAST, the following equation holds for each component
of the studied mixture based on an analogy with Raoult’s law:
pyi = xi pi(p),
(2)
where p is the total pressure in the bulk gas phase, pi is the bulk
pressure of component i that corresponds to the spreading
pressure p of the binary mixture; and xi and yi have been
explained above (eqn (1)). Since the molar fractions of the
adsorbed species sum to one, eqn (2) can be written as
py1 py2
þ
¼ 1;
p1
p2
(3)
for each component; pi and p are related through
ð pi
pA
ni ðpÞ
¼
dp;
RT
0 p
(4)
where A is the surface area of the adsorbent, R is the universal
gas constant, T denotes temperature, and ni ( p) is the amount
adsorbed at pressure p.
Levan and Vermeulen used eqn (2)–(4) together with the
single-component Langmuir isotherms to derive an explicit and
thermodynamically consistent binary Langmuir isotherm.39,40 The
adsorption isotherm of each pure component is simulated individually using GCMC. Then it is fitted using the Langmuir isotherm
n0i ¼
n0i;max Ki p
;
1 þ Ki p
3. Results and discussion
3.1.
SO2–CO2 mixture
Fig. 1 shows the adsorption isotherms of a mixture of SO2 and
CO2 at a molar ratio of 5 : 95 on a bundle of 3 nm diameter
DWCNTs as a function of the total bulk pressure. For CO2 (Fig. 1a),
the system with d = 0.5 nm shows the highest adsorption in
the studied pressure range. The reason is the direct relationship
between d and adsorption energy, and the inverse relationship
between d and accessible volume. The competing effects of
adsorption energy and adsorption space volume cause d = 0.5 nm
to be the optimum intertube distance for having the maximum
adsorption in this pressure range (0.1 bar o p o 2.5 bar). The
bulk partial pressure of CO2 ( pCO2) varies with the total pressure of
the particle reservoir. It is in the range 0.095 to 2.375 bar. The
optimum intertube distance, within this partial pressure range,
for the maximum adsorption amount is similar to that of pure
CO2.26 For SO2 (Fig. 1b) at low pressure p o 0.5 bar, d = 0 has the
highest adsorption because there is a strong interaction between
SO2 molecules and CNT walls in the interstitial and groove
regions when d = 0. Since the partial pressure of SO2 is very low
(0.005 bar o pSO2 o 0.025 bar), these regions have enough
volume to accommodate the SO2 molecules. As the pressure
increases to B0.5 bar (partial pressure of SO2 is B0.025 bar),
the intertube volume is saturated and the optimal intertube
distance is slightly shifted up to d = 0.5 nm. This trend
continues up to the highest studied pressure in the present
work ( p = 2.5 bar) and CNT arrays with d = 0.5 nm have the
highest adsorption between 0.5 bar and 2.5 bar. It is expected,
however that a further increase of pressure will shift the
(5)
where n0i,max is the monolayer capacity, Ki is the constant in the
Langmuir isotherm and n0i is the adsorbed amount of component
i in a single-component system. The fitted parameters and
eqn (2)–(4) are used to calculate the adsorption of component i,
ni, in a binary mixture
n1 ¼
QP1
1 þ P1 þ P2
þ n01;max n02;max
n2 ¼
P1 P2
ðP1 þ P2 Þ2
QP2
1 þ P1 þ P2
þ n02;max n01;max
P1 P2
ðP1 þ P2 Þ2
lnð1 þ P1 þ P2 Þ;
(6)
lnð1 þ P1 þ P2 Þ:
(7)
The dimensionless parameter Pi* is defined as Pi* = Ki pi, and Q is
the weighted monolayer capacity and can be calculated using
Q¼
n01;max P1 þ n02;max P2
:
P1 þ P2
4114 | Phys. Chem. Chem. Phys., 2016, 18, 4112--4120
(8)
Fig. 1 Excess adsorption isotherms of (a) SO2 and (b) CO2 in a SO2–CO2
(5 : 95) binary mixture system on double-walled carbon nanotube arrays,
with an inner tube diameter 2R = 3 nm and an intertube distance d = 0–
2 nm. T = 303 K. Pressure refers to the total pressure of the SO2–CO2
mixture.
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optimal intertube distance to even higher values, as seen in
earlier work for the adsorption of pure SO2.11 Moreover, it was
found in the earlier studies11,26 for a pure SO2 system, that
the maximum adsorption at low pressures is achieved for
d = 0.3 nm11 and d = 0.526 nm. Our results do not contradict
these findings, since the lowest pressure studied in the previous
studies was pSO2 B0.1 bar, but not the very low pressure region
(0.005 bar o pSO2 o 0.125 bar) of this work. Furthermore, our
results confirm the previous finding that the optimum intertube
distance depends on the applied pressure and the optimum d is
shifted to higher values with increasing pressure.11
As expected, for all conditions CO2 has higher adsorption
than SO2 due to its higher bulk concentration (95 mol%).
However, the selectivity of SO2 over CO2 shows a non-uniform
behavior (Fig. 2). When d = 0, the system shows the highest
selectivity (SSO2/CO2 = 16) at very low pressure, since molecules
perfectly fit to the narrow intertube pores of DWCNTs. Increasing
the pressure to p = 0.7 bar leads to a decrease of the selectivity to
around 8. With a further increase of the pressure, the selectivity
remains almost constant (SSO2/CO2 B 8). The situation for the
intertube distance of d = 0.5 nm is almost reversed. The selectivity
increases strongly with pressure up to p = 0.7 bar, then it
continues increasing but very smoothly. As a result, the two
curves cross at p B0.8 bar. The two systems with d = 1 and
2 nm show a behavior qualitatively similar to d = 0.5 nm. The
selectivity increases smoothly over the whole studied pressure
region, but does not exceed 6. Consequently, at lower pressure
( p o 0.8 bar) d = 0 has the highest selectivity, while the highest
selectivity at higher pressure (0.8 bar o p o 2.5 bar) is found for
the system with d = 0.5 nm. The selectivity found by Wang et al.25
for SWCNTs with similar inner diameters (2R = 2.71 nm) varies
from B10 to B20 at different pressures and it is obviously higher
than that found in the present study for DWCNTs. This is most
likely due to the higher outer diameter of our DWCNTs (2Rout =
3.66 nm) and consequently, their larger intertube volume which
leads to a decrease in adsorption energy. Moreover, it was also
reported for single-gas adsorption that SWCNTs show higher
adsorption than DWCNTs.41 DWCNTs, however, are still attractive from an application view point, since SWCNTs are expensive
and more difficult to synthesise.42 Moreover, the selectivity value
is found here to range from 4 to 16, indicating that the optimization of the pore size tuning can increase it by 4 times.
At low pressure, CO2 and SO2 may adsorb separately without
interfering with each other.43 In order to verify this assertion,
separate simulations are performed for pure SO2 and CO2 with
the pressure same as the partial pressure in the binary mixture.
Fig. 3 shows the SO2 and CO2 adsorption as a function of
their partial pressure in three different situations: a singlecomponent system, a binary system and IAST prediction. When
d = 0, the IAST prediction does not agree with the simulation
data, neither for CO2 nor for SO2. This means that, in the
adsorbed phase, SO2 and CO2 molecules do not behave as an
ideal mixture because of their high density in the low intertube
space volume of this geometry. The GCMC results show higher
SO2 adsorption and lower CO2 adsorption than the IAST prediction, reflecting the high selectivity for SO2 of this system
(Fig. 2). Furthermore, the adsorption of single gases deviates
markedly from the adsorption of each component in the binary
mixture. Thus, the assumption that each gas is adsorbed
separately without interfering with the other is evidently not
true in the CNT arrays with d = 0. There are also deviations
between IAST predictions and the GCMC adsorption isotherms
Fig. 2 Selectivity of SO2 over CO2, computed by the GCMC method, in a
SO2–CO2 (5 : 95) binary mixture on double-walled carbon nanotube
arrays, with the inner tube diameter 2R = 3 nm and the intertube distance
d = 0–2 nm. T = 303 K.
Fig. 3 Comparison of different methods in calculating the adsorption of
SO2 (left column) and CO2 (right column) in a binary mixture system on
double-walled carbon nanotube arrays, with the inner tube diameter
2R = 3 nm and the intertube distance d = 0–2 nm. T = 303 K.
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of single gases because the IAST predicts that each component
occupies a certain amount of volume and as a result, the
accessible volume in the IAST prediction for the other component is less than in single-gas systems. With increasing intertube distance, IAST predictions for the adsorption isotherms
move closer to the simulation results, so that for d = 2 nm, the
difference between adsorbed amounts predicted by IAST and
simulation is less than 5% for CO2 at pCO2 = 2.375 bar and also
for SO2 at pSO2 = 0.125 bar. This is due to the reduction of the
gas density with increasing intertube distance. Adsorption
isotherms of the binary system and single-component systems
show the same trend with increasing d. For instance, at pCO2 =
0.66 bar, the deviations between the adsorption of CO2 in the
binary system and the single-component system are 13%, 8%
and 7% for d = 0.5 nm, 1 nm and 2 nm, respectively. Moreover,
for d 4 0, there is only a small deviation between the adsorption
isotherms of the binary system and that of a single-component
system at low pressure (e.g. for CO2, d = 2 nm, at pCO2 = 0.38 bar,
the deviation is B5%). Increasing the pressure enhances the
deviation so that for d = 2 nm, at pCO2 = 2.375 bar, the difference
between adsorption in the binary system and the singlecomponent system is B13%. Therefore, at very low pressure,
the two gases behave independently. However, at higher pressure,
each gas occupies a considerable amount of volume and
reduces the accessible volume for the other one and, hence,
the presence of one gas has a detrimental effect on the
adsorption of the other.
Paper
Fig. 4 shows the density profiles of CO2 and SO2 in systems
with different d and p. The density profile inside the CNT is
indifferent to d, as has been observed before for pure CO2 and
SO2 adsorption.11,14, In all systems, a layer of CO2 and SO2
forms at low pressure ( p = 0.4 bar). This layer grows in density
with increasing pressure. Outside the CNT, when d = 0, the
density of SO2 is higher than that of CO2 at low pressure. As the
pressure increases, the density of SO2 remains almost constant
but the density of CO2 increases, confirming what has been
observed for the selectivity in Fig. 2. The reduction in selectivity
is due to the outer intertube volume being small and SO2 being
a large molecule. Therefore, the intertube volume saturates
soon. The CO2 molecules are smaller and they can fit themselves
in the remaining space. For d = 0.5 nm, the densities of both CO2
and SO2 increase with pressure. The increase is larger for SO2
than for CO2, because the intertube space is larger, and SO2
molecules interact strongly with CNT carbon molecules than
CO2. A similar behavior is observed for the case of d = 1 nm.
3.2.
SO2–N2 mixture
Fig. 5 presents SO2 and N2 adsorption isotherms of a SO2–N2
(1 : 99) mixture. When d = 0, a remarkable increase of SO2
adsorption can be seen until p B0.4 bar. Beyond that, the
adsorption approaches saturation with a lower rate. Increasing
d leads to a drastic reduction in SO2 adsorption and, hence,
d = 0 has the highest adsorption in the studied pressure region.
This is due to the strong interaction between SO2 molecules
Fig. 4 Density profiles for SO2 (red) and CO2 (black) adsorption in a binary mixture (5 : 95) on double-walled carbon nanotubes, with the inner tube
diameter 2R = 3 nm and the intertube distance d = 0–1 nm, at fixed pressure ( p = 0.4, 1 bar and p = 2.5 bar, left to right). T = 300 K.
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Fig. 6 Selectivity of SO2 over N2, computed by the GCMC simulations, in
a binary mixture (1 : 99) on double-walled carbon nanotube arrays, with
the inner tube diameter 2R = 3 nm and the intertube distance d = 0–2 nm.
T = 303 K.
Fig. 5 Excess adsorption isotherms of (a) SO2 and (b) N2 in a binary
mixture (1 : 99) on double-walled carbon nanotube arrays, with the inner
tube diameter 2R = 3 nm and the intertube distance d = 0–2 nm.
T = 303 K.
and CNT walls in the intertube space and also to the very low
partial pressure of SO2 ( pSO2 o 0.025 bar), which causes the
limited intertube space to be large enough to accommodate the
few SO2 molecules. This result is in line with SO2 adsorption
isotherms in the SO2–CO2 system (Fig. 1), where d = 0 also has the
maximum adsorption at low partial pressure ( pSO2 o 0.025 bar).
For N2, d = 0 shows the lowest adsorption because most of
the available volume, especially in the groove and interstitial
regions, is occupied by SO2 molecules which have stronger
interactions with CNTs. However, N2 adsorption increases
uniformly with pressure, since N2 molecules are smaller than
SO2 and they fit in the accessible space between SO2 molecules.
Increasing the intertube distance slightly to 0.5 nm has two
important consequences. Firstly, the intertube volume increases
and secondly, the density of SO2 molecules decreases. As a result,
there is more space accessible for N2 molecules. Therefore, N2
adsorption is notably higher at d = 0.5 nm than at d = 0. A further
increase in the intertube distance reduces the interaction
between N2 molecules and DWCNT carbons which causes a
decrease in the adsorption of N2.
The adsorption of N2 is generally less than SO2 in all systems,
although the bulk concentration of N2 is much higher than SO2.
To investigate the reason we calculate the minimum energy of
one single SO2, CO2 and N2 molecule inside the CNT. For this
purpose the probability of the Monte Carlo moves, displace, rotate,
and insert/delete, is changed to 0.7, 0.3 and 0.0, respectively, and
the simulation is carried out at low temperature (5 K). The
minimum adsorption energies are 13 kJ mol1, 22.6 kJ mol1
and 27.4 kJ mol1 for one N2, CO2 and SO2 molecule, respectively. Thus, the observed selectivity for SO2 (Fig. 6) is mainly
caused by the interaction of individual molecules with the CNT.
The selectivity for the system with d = 0 increases initially with
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pressure, reaching a maximum of more than 1600 at p = 0.25 bar.
Further increase of pressure leads to a decrease in selectivity, but
at p = 2.5 bar it is still B400. This is due to the fact that SO2 is a
large molecule with a strong interaction with CNT. Therefore,
SO2 molecules fill the intertube space soon at low pressure
( p o 0.4 bar) and saturate the system. On the other hand, the
small N2 molecules can be accommodated between SO2 molecules
and thus, N2 adsorption shows a monotonic increase as a function
of pressure. The selectivity for the system with d = 0.5 nm increases
smoothly from B80 to B140 with pressure. The selectivities of the
other systems are almost constant (SSO2/N2 B 55 and B45 for
d = 1 nm and 2 nm, respectively) in the studied pressure region.
A comparison between GCMC simulations and IAST predictions in the SO2–N2 system is shown in Fig. 7. As for the
SO2–CO2 system, IAST cannot predict the adsorption very well
for d = 0. Because of the high density in the intertube space, the
mixing behavior of the adsorbed gases is far from ideal. For
larger d, the gas density decreases and as a consequence the
IAST predictions become more similar to the adsorption calculated using simulations. Furthermore, the IAST predictions and
GCMC results of the SO2–N2 mixture agree better than those of
the SO2–CO2 mixture because of the weaker interaction of N2
with either SO2 or CNT carbons than that of CO2.
3.3.
CO2–N2 mixture
Fig. 8 shows the adsorption of CO2–N2 (15 : 85) mixtures calculated using the GCMC method and IAST predictions. When
d = 0, there is an obvious deviation between IAST predictions and
GCMC simulations but it is much less than what is observed in
SO2–CO2 and SO2–N2 mixtures. Like the previous mixtures, in the
systems with d 4 0, the deviation between IAST and GCMC is less
than that of d = 0. At p = 2.5 bar, the maximum deviation is less
than 7% and 3% for CO2 and N2 respectively. In short, IAST can
predict the CO2–N2 mixture better than SO2–CO2 and SO2–N2
mixtures. This result is in line with previous work.19,21
Similar to the SO2–N2 mixture, in all 4 CNT arrays, CO2
shows higher adsorption than N2 although in the bulk, there is
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Fig. 9 Selectivity of CO2 over N2 (15 : 85), computed by the GCMC
method, in a binary mixture system on double-walled carbon nanotube
arrays, with the inner tube diameter 2R = 3 nm and the intertube distance
d = 0–2 nm. T = 303 K.
Fig. 7 Comparison of excess adsorption data from IAST and GCMC
simulations: SO2 (left column) and N2 (right column) in a binary mixture
(1 : 99) on double-walled carbon nanotube arrays, with the inner tube
diameter 2R = 3 nm and the intertube distance d = 0–2 nm. T = 303 K.
d = 0 has the highest selectivity. With increasing pressure, the
limited adsorption space in this region causes the selectivity to
decrease from around 70 to around 40 at p = 2.5 bar, which is
still high. Unlike for d = 0, an increase in the pressure enhances
the selectivity of CNTs with d = 0.5 nm. Nevertheless, the
selectivity of this system is much lower (B20) than that with
d = 0. For larger d, the system shows an almost constant
selectivity (B15 and B13 for d = 1 nm and 2 nm, respectively)
in the studied pressure range and it is lower than for the two
shorter intertube distances. Moreover, the observed selectivity
of CO2 over N2 for optimized DWCNTs is higher than what has
been reported for zeolites (between B10 and B30 depending
on the type of zeolite and the pressure) and MOFs (between
B5 and B40 depending on the type of MOFs and the pressure).36,44
3.4.
Fig. 8 Excess adsorption isotherms of CO2 and N2 in a binary mixture
system on double-walled carbon nanotube arrays, with the inner tube
diameter 2R = 3 nm and the intertube distance d = 0, 0.5 nm, 1 nm and
2 nm. T = 303 K.
more N2 than CO2. This is due to the stronger interaction
between CO2 and CNTs (cf. Section 3.2). Moreover, d = 0 shows
the highest difference between the N2 and CO2 adsorption. The
selectivity highlights this difference (Fig. 9). The system with
4118 | Phys. Chem. Chem. Phys., 2016, 18, 4112--4120
Ternary mixture
To represent flue gas composition more realistically, we calculated
the selectivity of a ternary mixture to CNT arrays with d = 0.5 nm
(Fig. 10). The molar ratio of N2–CO2–SO2 considered is
84.21 : 15 : 0.79, which is similar to ratios of studied binary
mixtures in the present work. The selectivity of SO2 over CO2
increases with pressure from B4.5 to B7. This trend is very similar
to what was observed for the SO2–CO2 binary mixture. This result
was expected, since the interaction between N2 and CNT is very
weak in comparison with that between either SO2 or CO2 and the
CNT. Thus, N2 does not have an influence on the selectivity of SO2
over CO2. The selectivity of SO2 over N2 (and CO2 over N2) in a
ternary mixture shows the same trend as in a binary mixture. The
selectivities increase with pressure, however, in a ternary mixture,
SSO2/N2 (SCO2/N2), they are apparently higher than in a binary mixture.
The presence of two species (CO2 and SO2), which are both more
adsorptive than N2, leads to an additional crowding-out of N2 from
adsorption sites and, as a result, higher selectivities.
4. Conclusion
In this work, we used grand-canonical Monte Carlo simulations to
study the adsorption and separation properties of parallel-aligned
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Fig. 10 Selectivity of SO2 over CO2 (right), SO2 over N2 (middle) and CO2 over N2 (left), computed by the GCMC method, in ternary and binary mixture
systems on double-walled carbon nanotube arrays, with the inner tube diameter 2R = 3 nm and the intertube distance d = 0.5 nm. T = 303 K.
DWCNTs for flue gas mixture components (SO2, CO2, and N2)
at 303 K. Bundles of DWCNTs with a constant inner diameter of
2R = 3 nm but different intertube distances of d = 0–2 nm were
studied.
The quantity and quality of the selectivity for each system
depend on the type of adsorbate molecules and also on the
adsorbent structure. For SO2–CO2 mixtures, the adsorption of
CO2 and SO2 as a function of the intertube distance is nonlinear. As a result, at low pressures p o 0.8 bar, bundles whose
tubes touch each other (d = 0) show the highest selectivity
towards SO2. For higher pressures, bundles with a finite but
short intertube distance (d = 0.5 nm) show the highest selectivity.
For SO2–N2 and CO2–N2, on the other hand, no such pressure
dependence is found and close-packed CNT bundles (d = 0) have
the maximum selectivity towards SO2 and CO2, respectively, over
the whole studied pressure range. The selectivity relates directly
to the difference in the strength of interaction between each gas
species and CNTs. The highest difference and consequently, the
highest selectivity are observed between SO2 and N2, followed by
CO2 and N2, and finally SO2 and CO2. The lowest and the highest
observed selectivities are 4 and 16 for SO2–CO2, 50 and 1600 for
SO2–N2, and 10 and 70 for CO2–N2, respectively. The overall
picture does not change for a ternary mixture of all three
gases, because the adsorption of N2 is so much weaker than
the other two gases that their adsorption equilibria are not
influenced by the presence of N2. The selectivity results
indicate that firstly, DWCNTs are excellent materials for gas
purification and secondly, optimizing the pore structure is very
important to achieve the highest selectivity. Fortunately, closepacked bundles are easy to obtain45 and show the highest
selectivity in most cases.
The IAST predictions fail in predicting the adsorption for
mixtures involving SO2, in particular when d = 0. Increasing
d reduces the deviation between IAST and GCMC in SO2–CO2
and SO2–N2 binary mixtures. Nevertheless, the results are still
not in agreement, indicating that IAST is not suitable for the
systems containing strongly interacting molecules like SO2. In
the case of CO2–N2, the IAST and GCMC are in good agreement
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and like the other two systems, as d increases, the deviation
between GCMC and IAST reduces.
Acknowledgements
MR would like to thank Sadanandam Namsani for valuable
comments and discussion. JKS thanks the Alexander von
Humboldt Foundation and the Ministry of Earth Sciences,
GOI, for financial support. This work was supported by the
Priority Programme 1570 Porous media with well-defined pore
structure in chemical engineering: Modeling, application, synthesis
of Deutsche Forschungsgemeinschaft.
References
1 F. L. Darkrim, P. Malbrunot and G. P. Tartaglia, Int.
J. Hydrogen Energy, 2002, 27, 193–202.
2 J. Zhao, A. Buldum, J. Han and J. P. Lu, Nanotechnology,
2002, 13, 195–200.
3 X. Ren, C. Chen, M. Nagatsu and X. Wang, Chem. Eng. J.,
2011, 170, 395–410.
4 M. J. O’Connell, Carbon Nanotubes: Properties and Applications, CRC Taylor & Francis, Boca Raton, FL, 2006.
5 C. Lu, H. Bai, B. Wu, F. Su and J. F. Hwang, Energy Fuels,
2008, 22, 3050–3056.
6 A. I. Skoulidas, D. M. Ackerman, J. K. Johnson and D. S.
Sholl, Phys. Rev. Lett., 2002, 89, 185901.
7 L. Huang, L. Zhang, Q. Shao, L. Lu, X. Lu, S. Jiang and
W. Shen, J. Phys. Chem. C, 2007, 111, 11912–11920.
8 S. Furmaniak, A. P. Terzyk, P. A. Gauden, P. Kowalczyk and
G. S. Szymański, Chem. Phys. Lett., 2013, 578, 85–91.
9 S. Jakobtorweihen and F. J. Keil, Mol. Simul., 2009, 35,
90–99.
10 P. Kowalczyk, S. Furmaniak, P. A. Gauden and A. P. Terzyk,
J. Phys. Chem. C, 2010, 114, 21465–21473.
11 Y. Yang, M. Rahimi, J. K. Singh, M. C. Böhm and F. MüllerPlathe, J. Phys. Chem. C, under review.
Phys. Chem. Chem. Phys., 2016, 18, 4112--4120 | 4119
View Article Online
Open Access Article. Published on 11 January 2016. Downloaded on 18/06/2017 03:25:42.
This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.
PCCP
12 Z. Nickmand, S. F. Aghamiri, M. R. Talaie Khozanie and
H. Sabzyan, Sep. Sci. Technol., 2014, 49, 499–505.
13 D. N. Futaba, K. Hata, T. Yamada, T. Hiraoka, Y. Hayamizu,
Y. Kakudate, O. Tanaike, H. Hatori, M. Yumura and S. Iijima,
Nat. Mater., 2006, 5, 987–994.
14 M. Rahimi, J. K. Singh, D. J. Babu, J. J. Schneider and
F. Müller-Plathe, J. Phys. Chem. C, 2013, 117, 13492–13501.
15 M. Rahimi, J. K. Singh and F. Müller-Plathe, J. Phys.
Chem. C, 2015, 119, 15232–15239.
16 S. Agnihotri, J. P. B. Mota, M. Rostam-Abadi and M. J. Rood,
Carbon, 2006, 44, 2376–2383.
17 M. Bienfait, P. Zeppenfeld, N. Dupont-Pavlovsky, M. Muris,
M. Johnson, T. Wilson, M. DePies and O. Vilches, Phys. Rev. B:
Condens. Matter Mater. Phys., 2004, 70, 035410.
18 A. L. Myers and J. M. Prausnitz, AIChE J., 1965, 11, 121–127.
19 X. Peng, X. Cheng and D. Cao, J. Mater. Chem., 2011, 21,
11259–11270.
20 R. Babarao, Z. Hu, J. Jiang, S. Chempath and S. I. Sandler,
Langmuir, 2007, 23, 659–666.
21 P. Kowalczyk, Phys. Chem. Chem. Phys., 2012, 14, 2784–2790.
22 J. J. Cannon, T. J. H. Vlugt, D. Dubbeldam, S. Maruyama and
J. Shiomi, J. Phys. Chem. B, 2012, 116, 9812–9819.
23 X. Peng, D. Cao and W. Wang, Chem. Eng. Sci., 2011, 66,
2266–2276.
24 K. Vasanth Kumar and F. Rodrı́guez-Reinoso, RSC Adv.,
2012, 2, 9671.
25 W. Wang, X. Peng and D. Cao, Environ. Sci. Technol., 2011,
45, 4832–4838.
26 M. Rahimi, D. J. Babu, J. K. Singh, Y.-B. Yang, J. J. Schneider
and F. Müller-Plathe, J. Chem. Phys., 2015, 143, 124701.
27 W. D. Cornell, P. Cieplak, C. I. Bayly, I. R. Gould, K. M. Merz,
D. M. Ferguson, D. C. Spellmeyer, T. Fox, J. W. Caldwell and
P. A. Kollman, J. Am. Chem. Soc., 1995, 117, 5179–5197.
4120 | Phys. Chem. Chem. Phys., 2016, 18, 4112--4120
Paper
28 G. Hummer, J. C. Rasaiah and J. P. Noworyta, Nature, 2001,
414, 188–190.
29 J. G. Harris and K. H. Yung, J. Phys. Chem., 1995,
12021–12024.
30 M. H. Ketko, G. Kamath and J. J. Potoff, J. Phys. Chem. B,
2011, 115, 4949–4954.
31 J.-C. Neyt, A. Wender, V. Lachet and P. Malfreyt, J. Phys.
Chem. B, 2011, 115, 9421–9430.
32 U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee
and L. G. Pedersen, J. Chem. Phys., 1995, 103, 8577.
33 D.-Y. Peng and D. B. Robinson, Ind. Eng. Chem. Fundam.,
1976, 15, 59–64.
34 P. Wattanaphan, T. Sema, R. Idem, Z. Liang and
P. Tontiwachwuthikul, Int. J. Greenhouse Gas Control, 2013,
19, 340–349.
35 A. Chakma, Energy Convers. Manage., 1995, 36, 427–430.
36 B. Liu and B. Smit, J. Phys. Chem. C, 2010, 114, 8515–8522.
37 W. Sun, L.-C. Lin, X. Peng and B. Smit, AIChE J., 2014, 60,
2314–2323.
38 X. Xu, C. Song, R. Wincek, J. M. Andresen, B. G. Miller and
A. W. Scaroni, Fuel Chem. Div. Prepr., 2003, 48, 162–163.
39 M. D. LeVan and T. Vermeulen, J. Phys. Chem., 1981, 85,
3247–3250.
40 A. Sharma, S. Namsani and J. K. Singh, Mol. Simul., 2014, 41,
414–422.
41 D. D. Do, H. D. Do, A. Wongkoblap and D. Nicholson, Phys.
Chem. Chem. Phys., 2008, 10, 7293–7303.
42 A. Aqel, K. M. M. A. El-Nour, R. A. A. Ammar and A. AlWarthan, Arabian J. Chem., 2012, 5, 1–23.
43 P. Kowalczyk, Phys. Chem. Chem. Phys., 2012, 14, 2784–2790.
44 B. Liu and B. Smit, Langmuir, 2009, 25, 5918–5926.
45 D. J. Babu, M. Lange, G. Cherkashinin, A. Issanin, R. Staudt
and J. J. Schneider, Carbon, 2013, 61, 616–623.
This journal is © the Owner Societies 2016